An analogy can be dawn between the motion of a
satellite in an elliptical orbit and a ball rolling up a ramp. The ball
starts at the bottom of the ramp with an initial velocity V. As it travels
up the ramp, the ball is slowed by the force of gravity until it comes to
a stop, at which point it falls back down the ramp. Likewise a satellite
has the greatest velocity at the lowest point of its orbit known as the
point of periapsis passage. In some sense this is the "bottom"
of the orbit. The satellite swings away from the planet until it reaches
the point of highest altitude and lowest velocity known as the apoapsis,
at which point it "falls back" toward the planet.

The faster the ball is traveling at the bottom
of the ramp, the higher it will go before it comes to a stop and falls back.
Likewise, the faster the satellite is traveling at periapsis, the further
out away from the planet it will swing before coming back. It therefore
stands to reason that if we could somehow slow the satellite down at the
point of periapsis passage it would not swing as far away from the planet
before coming back. By lowering the periapsis altitude into the Martian
atmosphere we slow the spacecraft down around the point of periapsis passage,
which lowers the altitude of the apoapsis. Over many orbits the height of
the apoapsis is reduced which makes the orbit less elliptical and more circular.

More Detained Explanation

The analogy of a ball rolling up a ramp and a satellite
in an elliptical orbit can be viewed in terms of kinetic energy (K.E.) and
potential energy (P.E.). The kinetic energy is the energy an object has
as a result of its motion with respect to a frame of reference. The potential
energy is the energy an object has a result of a displacement against an
opposing force field, which in this case is gravity. For the sake of this
discussion, the reference point for the ramp is the flat bottom portion.
The reference point for the orbiting spacecraft is the center of Mars.

At the bottom of the ramp, the ball has zero potential
energy and maximum kinetic energy. At the top of the ramp the ball is stopped
and therefore has zero kinetic energy. At this point it has traveled the
greatest distance through the gravitational field, and therefore has maximum
potential energy. In the orbit of the spacecraft around Mars, the potential
and kinetic energy never reach zero, but they do achieve minimum and maximum
values at periapsis and apoapsis. At periapsis the kinetic energy is greatest
and the potential energy is least. Conversely, at apoapsis the kinetic energy
is smallest and the potential energy is greatest. By dipping the spacecraft
into the atmosphere we slow it down, remove kinetic energy, and thereby
decrease the total energy of the orbiting spacecraft. The height of the
apoapsis must decrease since there is less energy available.

Controlling how deeply we plow into the Martian
atmosphere

It stands to reason that if velocity is added at
the periapsis it increases the height of the apoapsis, then if velocity
is added at the apoapsis it should increase the altitude of the periapsis.
In other words, if we nudge the spacecraft forward with thrusters at the
high point of the orbit (apoapsis), it will increase the altitude of the
low point of the orbit (periapsis). If we fire the thrusters in reverse
and slow the spacecraft down at the apoapsis, the height of the periapsis
will decrease and the spacecraft will dig more deeply into the Martian atmosphere.
By tweaking the spacecraft with small propulsive maneuvers at apoapsis we
can control how much areobraking takes place on the opposite side of the
orbit around the point of periapsis passage.

Mars
Global Surveyor (MGS) Aerobraking

Part 1: Aerobraking Background and "The Plan" Before the
Start of Aerobraking

Following capture of the MGS spacecraft into Mars orbit on 12 September
1997 Universal Time the Mars Global Surveyor Mission began an aerobraking
phase which was intended to last for four months. In this period the orbital
period was to be reduced from an initial value near 45 hours to near the
mapping orbit period of 1.96 hours. A low sun-synchronous, near-circular,
near-polar mapping orbit was selected for MGS because it allows uniform
coverage independent of latitude for almost all of the planet, permits high
resolution observations of the surface and allows separation of diurnal
and longitude variations in surface and atmospheric measurements. The use
of such orbits is common for terrestrial remote sensing spacecraft, but
they have not been previously used for planetary missions, despite the observational
advantages, because they are energy expensive.

A good way of examining the energy and velocity change (delta V) requirements
for such orbits and the difference between using chemical propulsion and
aerobraking to move from a large elliptical to a low circular orbit is to
compare the MGS and Mars Observer Missions. The mapping orbit at Mars was
intended to be the same for these two missions (Mars Observer was launched
toward Mars in 1992 an failed three days before entering Mars Orbit in August
of 1993). MGS carries two fewer instruments and will use aerobraking to
circularize the initial capture orbit about Mars rather than using a series
of chemical propulsive maneuvers as was planned for Mars Observer. The payloads
of these two missions differ by 81 kg but the launch mass of MGS was 2.4
times smaller (1060 versus 2572 kg) than that of Mars Observer and the chemical
propulsive V required to get from the capture orbit into the near-circular
mapping orbit is 11 times lower for MGS ( 125 versus 1367 m/s). The majority
of the difference in launch mass between MGS and Mars Observer spacecraft
is in the fuel and oxidizer required by Mars Observer for circularization
of the orbit. By using aerobraking for circularization, MGS was able to
use a much smaller and less expensive (by a factor of more than five) launch
vehicle. This $200 million saving is sufficiently dramatic that future Mars
missions which require a low circular orbit will likely take this approach,
as indeed the 1998 Mars Climate Orbiter has done.

The Magellan spacecraft at Venus was the first planetary spacecraft to
accomplish aerobraking, as a demonstration, in the summer of 1993. The success
of this demonstration was the predicate for the adoption of aerobraking
by MGS. Aerobraking by MGS differs from that used by Magellan in two important
respects. First, on MGS aerobraking will be done before the start of the
main mapping activity. Thus, aerobraking success is required if the full
set of mission objectives are to be met. Second, to be successful, not only
must the aerobraking procedure result in a circularization of the orbit
at the proper altitude, but it must be accomplished such that at its conclusion
the local time at the sunward equator crossing is within a few minutes of
2:00 PM with respect to the mean sun. This latter constraint, which is essential
for the science objectives of the experiments, requires that aerobraking
proceed in a deliberate manner without significant interruption. If a delay
in aerobraking occurs in the early phases, the motion of Mars around the
sun will cause the local time at the sunward equator crossing to be nearer
to noon than 2:00 PM. These two factors make aerobraking the most challenging
element of the MGS Mission.

The MGS spacecraft has been designed to meet these aerobraking requirements.
For the drag portion of each periapsis passage the solar arrays are canted
back from the direction of flow to create a dynamically stable configuration
with the center of pressure behind the center of mass of the spacecraft.
One of the panels of the solar arrays did not latch when deployed shortly
after launch last October. The solar array springs which currently hold
this array open are not strong enough, by a large factor, to hold this array
open against the torque generated by aerobraking. As a result this array
will be rotated to place the solar cell side into the aerodynamic flow during
aerobraking which will generate a torque tending to latch the panel and
the associated gimbal will be powered to hold the array in place. Additional
post-launch thermal testing of the qualification solar array and an equivalent
gimbal drive motor have validated the suitability of this approach. This
aerobraking configuration is shown in Figure 1

Figure 1Spacecraft Configuration for Aerobraking.
The +Y Side Solar Array has the Solar Cell Side Away from the Aerodynamic
Flow Direction
The -Y Side Array has the Cells into the Flow.

The design has a margin of 90% with respect to unpredictable changes
in atmospheric mass density at periapsis. This means that the spacecraft
can tolerate at least an unpredicted change of 90% in the periapsis density
without exceeding a heating constraint of 0.68 w/cm2 (given the 17 m2 projected
area of the spacecraft this corresponds to a maximum dissipation of 116
kilowatts near periapsis). This level of margin substantially exceeds the
level of density fluctuations experienced in the hundreds of periapsis passages
during Magellan aerobraking. However, the region where aerobraking will
occur on Mars (105 ±15 km) has not been well characterized on any
planet and the additional margin is prudent.

MGS began aerobraking in Southern spring and the historical record of
global dust storms indicates this is the most likely season for such storms
to occur (the record also indicates global storms do not occur every Martian
year). In such storms it is not the dust itself which is a concern, since
there is no evidence that it reaches anywhere near the altitudes at which
aerobraking will occur, but the increase in density at the aerobraking altitude
associated with the expansion of the atmosphere due to the atmospheric heating
induced by the solar heating of the dust. Examination of the record of atmospheric
temperature changes during the two global dust storms in 1977 observed from
the Viking orbiters provides examples of rapid increases in atmospheric
temperature associated with global storm development. Modeling of these
temperature increases, including the use of the Mars global circulation
model at the NASA Ames Research Center, indicates that the density at aerobraking
altitudes could increase by as much as a factor of ten in a time as short
several days following the start of a major storm. The circulation model
results also indicate that for a storm that originates in the southern hemisphere
on Mars, which has been the historical pattern, the temperature in the atmosphere
of the northern hemisphere will start to increase before the dust itself
crosses the equator and moves into that hemisphere. This is of importance
for MGS as the periapsis latitude is in the northern hemisphere at the beginning
of aerobraking and remains in that hemisphere for a major portion of the
aerobraking time period.

Since the aerobraking altitude selection is based on the anticipated
atmospheric density, the occurrence of a global dust storm necessitates
moving periapsis to higher altitude as the storm builds but does not necessarily
interrupt aerobraking. Anticipating this possible density change will be
accomplished using the spacecraft itself, some of the MGS science instruments,
terrestrial based measurements and measurements from the Pathfinder vehicle
on the surface of Mars. Doppler tracking of the spacecraft will be nearly
continuous during the aerobraking time period and the orbit determination
process will provide an estimate of the periapsis atmospheric density each
orbit. The spacecraft accelerometers are also able to provide density estimates
based on the drag induced deceleration imparted to the spacecraft. Images
from the Mars Orbiter Camera will be used to examine the planet for evidence
of dust storm activity. Spectral measurements from the Thermal Emission
Spectrometer will be used to monitor the atmospheric temperature. The spacecrafts
infrared based horizon sensor will also be used to track the time history
of atmospheric temperature and the Electron Reflectometer (part of the Magnetometer
experiment) will provide electron density information including the altitude
of the ionospheric peak electron density. From earth, passive microwave
measurements of Mars will be conducted to derive the trend of atmospheric
temperature with time and, for the early part of aerobraking, Hubble Wide
Field Planetary Camera images will be available until Mars moves too close
to the Sun. The Pathfinder lander will have been on the surface of Mars
for three months at the start of MGS aerobraking and the history it can
provide of atmospheric opacity and surface pressure will be very valuable
in providing an indication of increased dust activity. These many sources
of information on the Mars atmosphere will be used in a structured decision
process to make judgments about the near term behavior of the atmosphere
and the small propulsive maneuvers which are used to adjust the periapsis
altitude.

The four months of the aerobraking time period have been divided into
three sub-phases called walk-in, main and walk-out. In the walk-in phase,
the orbit periapsis is lowered from the capture orbit altitude of 263 km
to the altitude at which aerobraking will occur through a series of small
propulsive maneuvers. The spacecraft will remain at the aerobraking altitude
during the main phase for three months as the apoapsis altitude is slowly
lowered from 54,000 km to about 2000 km and the orbital period is reduced
under 3 hours. The final three weeks of aerobraking constitute walk-out
which reduces the apoapsis altitude to 450 km while slowly increasing the
periapsis altitude. The descending orbit node location will have rotated
from its initial position near 5:45 PM to nearly 2:00 PM. At this point
aerobraking is terminated with a maneuver which raises periapsis out of
the region of significant drag. Following the completion of aerobraking,
Mars gravity calibration measurements are conducted, final mapping orbit
adjustments are made and the spacecraft and instruments are prepared for
the start of mapping which will begin in March 1998. Mapping will continue
for a full Mars year (687 days) and be followed by a six month Mars relay
mission.

Part 2: What Really Happened, So Far

Aerobraking began on schedule three orbits following the entry of the
spacecraft into Mars orbit. The low point of the orbit (periapsis) was slowly
lowered deeper into the atmosphere and by orbit 11 the density at periapsis
was at the low end of the range needed (42 kg/km3 ). On this
single pass through the atmosphere the orbit period was lowered by one hour
and four minutes. On orbit eleven some motion of the damaged solar panel
(on the -Y side of the spacecraft) was noticed, using the sun sensor mounted
on this panel, which was consistent with the failure model that had been
developed. The -Y panel moved 4 degrees closer to the latched position.
On the next orbit (orbit 12) the panel moved all the way to the latched
position but there was no positive way to know if the panel latched or not.
Three orbits later at periapsis 15 the periapsis density abruptly increased
by 46%. This was not unexpected and as a consequence the spacecraft had
been designed to handle changes up to 90%, but several of the onboard sensors
indicated that the -Y panel had moved as much as 17 degrees on the other
side of the expected latched position. This could only mean that the failure
model developed in cruise was incorrect and that it would not be safe to
proceed further with aerobraking until the problem with the -Y solar panel
was better understood. At the next apoapsis (apoapsis 15) the periapsis
was raised to reduce the risk to the spacecraft an a careful examination
of all relevant data began. Because the MGS Mission was designed around
a 2:00 PM sun-synchronous orbit and the local time of the orbit equator
crossing was changing whether or not aerobraking was taking place. there
was great pressure to get back to aerobraking before to much time was lost.
However, after five days it was clear that a good understanding would take
more time and the Project Manager made the decision to raise the periapsis
altitude to about 172 km effectively ending aerobraking and freeing the
flight team to concentrate on understanding what had happened to the -Y
solar panel.

While the engineering assessment of the -Y solar panel was underway it
was also necessary to consider two additional questions: 1. What orbit should
the spacecraft be placed in if any further aerobraking was not possible?
and 2. What orbit should be set as a goal if aerobraking could continue
but only at a reduced level? Both of these questions involve understanding
the spacecraft capabilities in relation to the science instrument capabilities
and the scientific objectives of the mission. If no further aerobraking
was possible, the remaining propellant would only allow a modest reduction
in the orbit period, which by periapsis 18 had been lowered from the original
45 hours down to 35 hours and 24 minutes. Elliptical orbits are not very
useful for the type of science observations which were planned for the mapping
MGS mission because they provide very little time near the planet. The Mars
Orbiter Laser Altimeter (MOLA), for example, can only acquire a return signal
when the range to the surface is less than about 780 km. This range restriction
would mean that MOLA could acquire altimetry data for only about 26 minutes
each orbit whereas in the planned circular orbit it would collects data
continuously for a full Mars year (687 days). This is a difference of 508
hours versus 16,408 hours or a ratio of 1/32. This property of elliptical
orbits suggested that, if at all possible, aerobraking should continue to
allow a low circular orbit to be achieved. The next question involved whether
or not to try to achieve a sun-synchronous orbit and if so what should the
time of equator crossing be for such an orbit. Since the MGS spacecraft
was designed for a 2:00 PM sun-synchronous orbit it was quickly determined
that problems would arise with respect to power and communications if the
low circular orbit were free to drift in the time of equator crossing. Having
established that a sun-synchronous orbit was necessary, the equator crossing
time would need to be selected. Because aerobraking had been halted it was
no longer possible to reach the 2:00 PM equator crossing orbit and what
could be achieved depended on the outcome of the engineering evaluation.
When the spacecraft constraints (chiefly power and communications with earth)
were matched against the instrument viewing constraints it became clear
that the only acceptable equator crossing time that was still possible and
met all the requirements was 2:00 AM, essentially 180 degrees from the initial
2:00 PM choice.

Figure 2Complete Solar Array Showing the Gimbal which Attaches to the Spacecraft
The Yoke which Has Sustained a Crack Across One of its Face Sheets
The Inner Panel which is Covered with Solar Cells
The Outer Panel which is Also Covered with Solar Cells
A Drag Flap which was Added Late in the Design Cycle to Increase the Array
Drag Area During Aerobraking

The engineering assessment reviewed all relevant spacecraft telemetry
going back to the deployment of the solar arrays just after launch, testing
in the laboratory using a spare solar array that had been used to qualify
the design and extensive analysis. The result was a new model of the failure
which fit the spacecraft telemetry and the results of laboratory testing.
It appears that the -Y solar array was broken in the area of the yoke (See
Figure 2 below for the location and shape of the yoke). The yoke is the
portion of the array which attaches the two solar panels of the array to
the two axis gimbal which allows the array to articulate. The yoke and the
inner and outer solar array panels are made of composite material (two carbon
fiber/epoxy face sheets with an aluminum honeycomb sandwiched in between).
Apparently when the solar array damper failed during the deployment of the
-Y solar array shortly after launch, the momentum generated by the undamped
array was sufficient to crack one of the two face sheets comprising the
yoke near its attachment with the gimbal. The failure was duplicated with
the qualification array in the laboratory. With only one intact face sheet
aerobraking could resume but at only one third or less the rate previously
available (in terms of pressure on the vehicle at periapsis one third the
original rate translates into a dynamic pressure of about 0.2 N/m2
).

With the engineering assessment complete a decision was made to proceed
with aerobraking at lower densities and reduced pressure with the goal of
reaching a 2:00 AM sun-synchronous mapping orbit in early 1999. Because
Mars (and the spacecraft) would pass directly behind the sun in May 1998,
aerobraking would pause before this event (solar conjunction ) as it was
judged to hazardous to proceed with aerobraking if communications were uncertain
due to the proximity of the spacecraft to the sun. On 8 November 1997 (the
periapsis for orbit 36) the spacecraft resumed aerobraking after a pause
of just under four weeks. During this pause period (called the "Hiatus"
by the operations team) the science instruments were oriented toward the
planet at each periapsis and the science data collected formed the principal
basis for a series of scientific papers published in the magazine Science
on 13 March 1998.

The return to aerobraking was uneventful and for several weeks aerobraking
proceeded without incident at an altitude around 124 km above the surface
until Thanksgiving day, 26 November 1997 when at periapsis 51 the dynamic
pressure and atmospheric density increased by a factor or 2.33 or 133%.
In consultation with the Projects Atmospheric Advisory Group (this
group was responsible for providing a scientific assessment of the state
of the atmosphere on an orbit by orbit basis) it was quickly determined
that a regional dust storm in the Southern hemisphere of Mars (Noachis Terra
region, initially centered near 40° North, 20° East) was likely
responsible for the increase in atmospheric density experienced by the spacecraft
in the upper reaches of the atmosphere far to the North. Because the emergence
of such a storm would be expected to increase the atmospheric density by
even larger amounts as it developed, a decision was made to increase the
periapsis altitude such that the altitude for periapsis 52 was 132 km. The
Noachis storm never reached the size of the global storms observed by the
Mariner 9 and Viking spacecraft and no further increases in periapsis altitude
were necessary for MGS. In several weeks the effects of the storm began
to dissipate and by Christmas 1997 the periapsis altitude had been gradually
lowered back down to the 124 km level where it had been before the start
of the dust storm.

Since the start of aerobraking the periapsis latitude has been slowly
moving northward from an initial value around 32° North and by Christmas
it had increased to 42° North. During this same time period the sun
as observed from Mars was moving South and the Northern Martian polar region
was in perpetual darkness (Fall in the Northern Hemisphere of Mars). As
a consequence there was a tendency for the density at a constant altitude
to decline as the spacecraft moved North and indeed by the end of Aerobraking
Phase 1 near the end of March 1998 the periapsis had been moved down to
an altitude around 117 km for the same dynamic pressure at periapsis (i.e.
about 0.2 N/m2). Throughout aerobraking the spacecraft experienced
relatively large changes in periapsis density from orbit to orbit. These
changes were due to time dependent changes in atmospheric density and to
changes in atmospheric density with longitude. Since the period was constantly
being shortened during aerobraking there was no regular pattern in the longitude
of periapsis and time and longitude variations in density could not be separated.
One means of looking at the variation in atmospheric density experienced
by the spacecraft is to use the periapsis density and scale height (the
atmospheric scale height is a measure of how rapidly the atmospheric density
is changing with altitude) determined by the accelerometer team to derive
the density at a constant altitude and directly examine the orbit to orbit
variation as can be done using Figure 3.

Figure 3
The Density Measured at Each Periapsis is Extrapolated to a Constant Altitude
of 122 km and Plotted in this Figure For Orbits 80-150 (2 January 1998-27
February 1998). The Smooth Green Curve is a Least Squares Exponential Fit
to the Points Shown Illustrating the Slow Decline in Atmospheric Density
Experienced as the Spacecraft Periapsis Moved North.

For the 71 orbits shown in Figure 3 the mean value of atmospheric density
is 16.1 kg/km3 without removing the evident trend and the standard
deviation is 35.8%. By coincidence the pre-aerobraking estimate for the
standard deviation was equivalent to 35%. It is apparent from Figure 3 that
there are times when there is appreciable orbit to orbit variation in atmospheric
density which requires an orbit by orbit evaluation on the part of the flight
team to determine whether or not the periapsis altitude should be lowered
to maintain a steady decrease in orbit period or increased to avoid large
forces on the solar arrays.

One of the unanticipated results from aerobraking in the Northern hemisphere
of Mars is the discovery that there is a longitude dependence to the density
variations which is related to surface topography. Figure 4 displays this
variation.

Figure 4 The Extrapolated Periapsis Density at an Altitude Of
122 km as a Function of the Periapsis Longitude for Orbits 80-150. The Smooth
Green Curve is a Least Squares Fit to the Data Using a Constant Term, Two
Sin Terms One with a Period of 360 Degrees and One with a Period of 180
Degrees (i.e. two cycles in 360 Degrees).

Although the scatter in Figure 4 is large over the 71 orbits involved
it can fairly clearly be seen that the high density points are found around
the 90° and 270° degree longitudes and the low points tend to cluster
around the longitudes 0° and 180°. The pattern of highs and lows
in density has been stable for many orbits. The longitudes of 90° and
270° in the Northern hemisphere of Mars are noticeable higher topographically
than other longitudes and this suggests a coupling between the topography
and the density in the lower thermosphere at 122 km which represents a new
discovery.

While aerobraking was continuing the flight team refined plans for getting
the spacecraft into the mapping orbit by March of 1999. Because of solar
conjunction in May of 1998 aerobraking will be broken into two phases with
the first phase ending at the end of March 1998. At this time periapsis
will be raised to the 170 km altitude range and Phase 1 of aerobraking will
end. The second phase of aerobraking does not need to start until next September
so the intervening six months will be used for science observations with
the spacecraft pointing the instruments toward the planet at each periapsis.
This period is being called the Science Phasing Orbit and the orbit period
will be near ll.6 hours. For three weeks around solar conjunction in May
1998 communications with the spacecraft will be less reliable and science
observations will pause. During the Science Phasing Orbit the location of
periapsis will move North to within 3° of the North pole and then move
back down to about 60° North latitude. When aerobraking picks up again
in the fall about 700 more aerobraking orbits will be required to reduce
the orbit period to the desired 118 minute period and the spacecraft is
expected to be ready for mapping in March of 1999 one year later than planned
when aerobraking began. The original aerobraking plan involved about 300
orbits of aerobraking and the revised plan involves about 900. As this description
is being written (24 March 1998) the spacecraft has completed 196 orbits
about Mars since entering Mars orbit and the Science Phasing Orbit period
of the mission is about to begin.